Stepwise hierarchical clustering-assisted materials principal component analysis for semi-quantitative estimation of three-component inorganic materials

Abstract A stepwise hierarchical clustering-assisted materials principal component analysis (SHAMP) method was developed to provide a semi-quantitative estimate of mixture ratios in multicomponent inorganic materials. In this SHAMP approach, hierarchical cluster analysis was first utilized to coarsely classify clusters that encompass the original materials in the training dataset, followed by a stepwise application of principal component analysis (PCA) within each cluster at different hierarchical levels of the dendrogram. This study demonstrated the efficacy of SHAMP by using multi-elemental data obtained from inductively coupled plasma mass spectrometry (ICP-MS) for 2- and 3-component material models—SUS304, brass, and nichrome—allowing for spatial visualization of the mixture ratios in inorganic composite materials. PCA scores facilitated a semi-quantitative estimation of the mixture ratios, while triangular diagrams notably illustrated the mixing proportions of the original components in the 3-component materials. The significance and consistency of the principal components were confirmed through loading analysis and the meticulous treatment of values below the limit of quantification for each element. The SHAMP method proved to be an effective strategy for inferring the original material composition from mixture data derived from multi-elemental analysis such as ICP-MS.